Data synchronization with timing

This paper proposes and analyzes data synchronization techniques that not only resynchronize after encoded bits are corrupted by insertion, deletion, or substitution errors, but also produce estimates of the time indexes of the decoded data symbols, in order to determine their positions in the original source sequence. The techniques are based on block codes, and the estimates are of the time indexes modulo some integer T, called the timing span, which is desired to be large. Several types of block codes that encode binary data are analyzed on the basis of the maximum attainable timing span for a given coding rate R (or, equivalently, redundancy ρ=1-R) and permissible resynchronization delay D. It is found that relatively simple codes can asymptotically attain the maximum timing span among such block codes, which grows exponentially with delay, with exponent D(1-R)+o(D). Thus, large timing span can be attained with little redundancy and only moderate values of delay